There are two families of orthodox churches, Oriental Orthodox and Eastern Orthodox. The British Orthodox is part of the Oriental Orthodox family of churches. For the average layperson our belief is the same and we both have apostolic succession. The ethnicity associated with each church is roughly the country of origin but does not necessarily state which family it is from.
To be married in an Orthodox church, you will both first have to be baptized if you aren't already in an Eastern Orthodox, Oriental Orthodox, Roman Catholic church - some churches will also accept Anglican and Lutheran baptisms. Oriental Orthodox churches will likely have the quickest conversion (catechumen) process and will likely be the most tolerant of non-orthodox baptisms.
The Antochian Orthodox church is an Eastern Orthodox church and so is the Russian as well as the Greek and Ukrainian. Once you have converted you can receive the sacraments in any of these. Likewise if you join an Oriental Orthodox church, you can receive the sacraments in any of them - these are the Coptic, Ethiopian, Armenian, Syrian, Indian, and British Orthodox churches. You cannot flip flop between the Eastern and the Oriental with an actual conversion process in some cases.
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